Simplified analog dispatch computer



Oct. 24, 1961 Filed Oct. 29, 1957 leblzll' Statlon 2 Sfaion 5 E. L.HARDER SIMPLIFIED ANALOG DISPATCH COMPUTER 2 Sheets-Sheet 1 Fig.l.

0d- 24, 1961 E. L. HARDER 3,005,589

SIMPLIFIED ANALOG DISPATCH COMPUTER Filed Oct. 29, 1957 2 Sheets-Sheet 2Confrol Amplifier f49 e|||a| 48 45 qg "l 4@ SUOD l Confrol Amplifier.5S-J

Sfoiion 2 Y Y Control Amplifier 52? 57! 'l smon Control Amplifier TP 547,i

Fig. 2.

3,005,589 SIMPLIFIED ANALOG DISPATCH COMPUTER Edwin L. Harder,Pittsburgh, Pa., assignor to Westinghouse Electric Corporation, EastPittsburgh, Pa., a corporation of Pennsylvania Filed ct. 29, 1957, Ser.lNo. 693,099 Claims. (Cl. 23S-'185) This invention relates generally tosimplified analog computers and more particularly to an analog type ofcomputer capable of solving the economic dispatch of power amongstations of a power system.

Such systems generally include a plurality of interconnected electricpower generating stations forming a basic electrical network, havingconnections to various loads sometimes including tie-line connectionswith adjoining power systems. A computer of the type to be explainedherein, serves a purpose of providing the most economical method ofdividing the total load among a plurality of generating stations in thesystem.

It has been the general practice in computers of this nature to solvefor the condition of equal incremental delivered power cost to the loadfrom every variable generating station, including the two incrementalcost factors of (a) incremental production cost of the generatingstation, and (b) cost of incremental transmission loss between eachstation and the load. It has been proved that when incremental deliveredpower costs are equal from all variable stations, the lowest cost ofoperation exists. Computers of this nature necessarily become complexsince it is necessary to provide a matrix of incremental transmissionloss coeicients, n2 in number where n is the number of generating andtie stations. All n2 values must ybe changed to represent a change inthe transmission system. This is such a major operation that inpractice, the coeiiicients are changed only once or twice a year, when anumber of transmission changes have accumulated. It is not feasible tofollow transmission changes daily as they occur, and as is desired.

It is therefore an object of this invention to provide an analogdispatch computer of a greater simplified arrangement capable ofproducing satisfactorily dispatching results.

It is another object of this invention to provide an analog dispatchcomputer having a loss resistor of the proper value placed in thecomputer system in a position corresponding to each transmission line inthe actual transmission system.

It is another object of this invention to provide a simplied analogdispatch computer that is readily modified to include any changes in thepower system associated therein.

It is another object of this invention to provide an economic dispatchcomputer having a reference point selected in the computer correspondingto a point in the system to which all stations are balanced to have thesame incremental delivered power cost.

It is another object of this invention to provide an economic dispatchcomputer capable of eliminating the necessity of adjusting all stationsin the computer to the same average incremental delivered power costdirectly.

Other objects, purposes, and characteristic features will become clearas the description of this invention progresses.

As contracted with the equal incremental delivered power cost principleof the computers requiring an n2 matrix of loss resistors, this computerwill be based on another principle as follows. When the incrementalproduction cost ratio for each pair of generating stations is equal tothe incremental fraction of power delivered (i.e. 1-1/1 loss) from thelower cost to the higher cost station, the economic dispatch exists. Forexample, if 90% States Patent 0 3,005,589 Patented Oct. 24,` 196.1

of incremental power transmitted from station l to station 2 reachesstation 2, then station 1 should be operating at of the incrementalproduction cost of station 2 to be in economic balance. It can be shownthat this condition also is a necessary and suflicient condition foroperating cost. In particular, all generating stations can be related toany one point of the system, as for example a principal generating bus.As a first approximation, with power factor and voltage -both taken asone per unit, i.e. current and power are the same in per unit. The lossin a line connecting two stations is 12R of power transmitted. Theincremental loss di 2 dI(I R) l is 21R .per unit of power transmitted. Aline 4having 12R of 5% of transmitted power, has incremental loss of 10%of incremental transmitted power. Thus, l-ZIR is a close approximationto the fraction of incremental power delivered. This relationshoipIbetween the incremental loss 21R and the voltage drop IR is made thebasis of an analog computer in which the Voltage drops corresponding tothe power flow also becomes the increases ofA incremental productioncost as we proceed through the system network from station to station.The incremental production costs are also represented as D.C. voltagesbut in reverse sense, and the scaling is arranged so that the samenetwork represents power flow and required incremental production costfor economic operation.

As shown above when power is transmitted from one station to another ina system as substantially constant voltage, E, and with substantiallyunity power factor:

The power is P=EI l/ l of base values. The loss is L=I2R 1/ 1 of base-values. The incremental loss is 21R l/ l of base values.` Or theincremental loss is v1/1 of base values;

Y ZPR representing the fraction of incremental transmitted power loss,let E=1 then the equation becomes 2PR.

Let F1(P1) be the incremental production cost of station '1 and F2(P2)be `the incremental production cost at sta-tion 2 and let P1 2 be thetransmitted power then if F2022) (12RP1 2)=F1(P1) this system is ineconomic balance.

In practicing this invention, there is provided an economicdispatch'computer of the simplified form for a distribution systemAhaving '-the'network of a plurality v pose, -to be describedhereinafter.

of stations capable of taking the incremental cost of producing power ateach station in vthe system, and a value representing the total power ofeach station in vthe system .and interconnecting the total output ofeach of the stations into a network of transmission loss re- -sistors insuch a manner that at -a selected point in the system the cost ofproviding one unit of power from each of the stations in the system isthe same. With this impedance network, it is possible to refer theincremental costs of'producing power at veach station to the systemreference point, and thus adjust the output power of each station toproduce a balance of the unit cost at the reference point. With thisarrangement, the systems and each station in the system is then said tobe in an economic balance condition.

FIGURE 1 is a schematic .view of a simplified dispatch computer capableof'providing the economic power dispatch of an associated system; and

FIG. 2 is a schematic view of a servo controlled economic dispatchsystem capable of displaying automatically, the economic dispatch oflpower within a system associated therewith. t

In each of the views, similar parts bear like-refer.- ence characters.

The simplied computer of FIGURE l is a compu-ter that is manuallycontrolled for the purpose of indicating the most economical dispatch ofpower for each station in a power network. Since the computer can beconstructed to Yhave i-ts reference point at any desirable point in thesystem, the computer of'FIGURE 1 has been selected `to have stationl'bus point A as the refer ence in the system at which point, a unit ofpower delivered from any variable station in the system costs the same.The potentiometer CT may be a non-linear potentiometer similar to thatdescribed in the analog computer case Serial No. 556,149. led December29, 1955, invented by Edwin L. Harder and assigned to the commonassignee. The potentiometer CT is provided with a manual control knob 1and interconnected mechanical link 2 having secured thereto 4anindicator 3 divided into segments indicating the power generated by unit1, and two additional potentiometers 2q and 2b necessary to satisfy theload requirements of the system. The potentiometer CT is also providedwith a source of voltage 4 connected thereacross to develop -a voltageacross the potentiometer to be delivered to the conductor 5 with respectto conductor 11 for a pur- The potentiometers 2a and 2b provide a meansof delivering a voltage to each station that is proportional to thesystem needs to be explained hereinafter.

Similarly, station 1 is provided with a manual control knob 6 and amechanical linkage 7 interconnecting a power indicating dial 8 pointer9, a potentiometer P1 representing the power output of station '1 and anincrementalV costs potentiometer C1. With the two potentiometers P1 andC1 tied together and connected to the pointer 9 of the power indicator 8and the manual control knob 6, it can be seen that a rotation of themanual control knob 6 and its mechanical link 7 displacing thepotentiometer P1, representing the total output power of station l, alsoYchanges the value of the incremental cost of producing the power atstation 1. Power potentiometer P1 at 'station l is provided with abattery or other suitable source of power 10 connected -thereacrossthrough the .potentiometer 2a to produce a voltage on the variablepotentiometer P1 representative of 7the' total power produced by thestation. Likewise, the potentiometer C1 is connected across thepreviously mentioned source of power 4 by .the conductors 11 and 12.Potentiometers C1 like CT may be, if necessary, a nonalinear type ofdevice capable of' producing output voltages representative of theincremental worth of delivered power :at station .1. Stations Z land BofY this -disclosed three-station network are provided with theVpotentiometers P2 and P3 respectively, also connected across the sourceof power 10 by the potentiometer 2a and the' conductors 13 and 14, sothat the voltages received from the variable taps of the potentiometersP2 and P3 represent the total power output of the stations 2 and 3,respectively. Like station l, stations 2 and 3 are provided with apotentiometer indicating the value or incremental cost value ofproducing power at each of these stations. These are designated C2 andC3 respectively. Station 2 like that -of station 1, has its twopotentiometers, P2 and C2, interconnected by a mechanical link 15 whichis also connected to ya pointer 16 of a power indicator dial 17 and amechanical hand knob 18 for providing a means of rotating the mechanicallink 15 and its connected indicator pointer 16 and its potentiometer P2and C2. It is Valso pointed out 4that C2 is connected across the sourceof power 4 by the conductors 11 and 12. Station 3 has its powerproducing potentiometer P3 and its incremental worth of delivered powerpotentiometer C3 interconnected by a 'mechanical link 19 which alsocarries a pointer 26 of a power indicating dial 21. The mechanical link19 is also'provided with a hand rotating knob 22 capable of changing theposition of the variable taps of the power potentiometer P3 and thepotentiometer C3 in a manner similar to that previously described.

Similar to the previously mentioned stations'l and 2, the conductors 13and 14 serve to connect the potentiometer P3 of station 3 across thesource of voltage 10 through the potentiometer 2a. Likewise, theconductors 1'1 and 12 serve -to connect the potentiometer C3 across thesource of voltage 4, in a manner similar to the C poten-tiometers instations 1 and 2. The remaining power-producing 'or consuming point inthe system is the tie-point called TF1. Since the tie-point is a point owhich power may be delivered from the system to an adjacent system oract to receive power from an adjacent system and thus supply the powerto its associated system, it is only necessary to provide a meansofindicating total power means supplied or received between this systemand the adjacent system. For this purpose, we provide the potentiometerPT connected across the source of power 10 and an additional source ofpower 23 connectedr in series. Y lf we assume that the Vsource of power10 is equal in potential to the source of power 23 and with the twosources connected in series across a power potentiometer PT, that withthe potentiometer in its center or neutral position, an indication ofzero power supply or delivery through the tie-point would berepresented. This source 10 and Z3 arrangement with the potentiometer 2aand 2b allows the system unit potential to be varied withoutaiecting'the tie-power representation set by potentiometer PT. Thebattery '10 is connected across the potentiometer 2a, the battery 23is'connected across the potentiometer 2b and the wiper arm of thepotentiometer 2a is connected to one side of the potentiometer PT whichthe wiper arm of the potentiometer 2b is connected to the other side ofthe potentiometer PT.

In order to yrepresent the power generated, the power used and the powerlost in the system, the network of resistances interconnectingthepreviously described potentiometers is provided. In order to provide asimplified system capable of ignoring minor variables inthe system forthe purpose of producing a computer that is simple in structure, it isnecessary to proportion the network resistances in such an arrangementthat the ignored vari ables become minor factors in the computingsystem. For this reason the current generating rsistances GT and G2 andG3 connecting the power output tap members of the potentiometers P1, P2,and P3 respectively'to their loads RLT and RL2, and RLa, respectively,as well as network loads, are made of very high resistance so thatcurrents owing will be proportional to' the voltages developed betweenpointers of potentiometers P1, P2 and P3, and common point M, as limitedonly by current generating resistors G1, G2 and G3, respectively.

Since the loads of the network are not necessarily located adjacent tothe generating stations, the loads RL4 and RL5 have been included torepresent loads taken from the transmission lines at points betweengenerating stations. Each of the resistors R1 through R11 represent lineloss resistances for the transmission lines in the system. Each resistorR1 through R11 is an actual representation of a transmission line in thesystem and for this reason it is simple to change the operation of thecomputer to agree with the system if the system should be modified bythe removal or the addition of a transmission line between any twopoints in the system. For example, if the transmission line betweenpoint 24 and point 25 in the system was to be removed, an elimination ofresistor R1 within the computer would also be necessary. It can be seenthat power delivered by stations l, 2 and 3 to the network of resistorsrepresenting the transmission system and loads, are provided withparallel return paths through the parallel transmission lines andparallel loads. For example, power delivered to point A by station 1 hasa return path through a load resistor RL1 as well as a parallel returnpath through the transmission lines represented by the loss resistor R1to point 25 through the load RL.1, a transmission line represented bythe loss resistor R2 and through load RL5 as well as additional pathsthrough other transmission lines such as those represented by the lossresistors R1 and R5 and through other load resistors such as RL2.

A typical operation of the system will now follow:

if the operator of this computer determines and adjusts the manualcontrol knob 1 to the incremental cost of power setting necessary forthe system, the incremental cost potentiometer CT assumes the conditiondictated by manual control knob 1, and thus delivers a voltage withrespect to bus 11 through the conductor 5 to point A of the systemnetwork. Since point A is the point of which station 1 delivers itsrepresentative power to the network, the operator will observe thenullmeter N1 connected between the C1 potentiometer and point A todetermine the direction and the amount of adjustment necessary toprovide adequate power output from station 1. Adjustment of the knob 1also adjusts the potentiometers Za and 2b to provide a critical propervoltage supply to the potentiometers P1 through PT. If the operatorobserves the nullmeter N1 in a position indicating unbalance, the manualcontrol knob 6 is rotated until the null N1 is again at zero, or abalanced condition. As the manual control knob 6 is rotated thepotentiometer P1 delivers the necessary voltage to the currentgenerating resistor G1 and consequently the necessary current to point Ain the system network. At this time it can be said that station 1 is nowin economic balance with incremental cost potentiometer CT indicatingincremental cost for the reference bus, station l. The power of station1 can now be read from the indicator 8.

The operator now goes to station 2, observes the nullmeter N2 locatedbetween the variable tap of the potentiometer C2 and the point 26corresponding to station 2 bus in the system network. If the nullmeterindicator N2 indicates that station 2 is not providing its share of theload, the operator then rotates the manual control knob 1S readjustingthe potentiometer P2 to a new level to supply the power through thecurrent generator G2 to the point 26. Adjustment is continued untilnullmeter N2 indicates a balance between the incremental worth ofdelivered power at station 2 represented by the potentiometer C2 and thevalue required to be in balance with station 1. It is pointed out atthis time that when the nullmeter N2 is adjusted to a null position, theincremental cost of power delivered to the point 26 is balanced againstthe incremental worth of delivered power C2 at station 2, and when thisis referred through the loss resistors to point A, the cost of powerdelivered to point A 6 by station 2' is the same as the cost of powerdelivery by station 1. Also, this is a lirst trial setting and will haveto be adjusted after station 3 has been set.

The same procedure is followed with respect to station 3 in order togain a null on the null indicator N3 connected between the variable tapof the incremental worth of delivered power potentiometer C3 associatedwith station 3, and the point 27 corresponding to station 3 bus.

Since the tie-point TP1, is a xed rate of cost per unit of powersupplied or delivered, it is not necessary to determine the incrementalworth of power in the setting of the potentiometer PT by the manualcontrol knob 29. A power position of zero which is indicated by theindicator 30 is a position of zero power received or delivered throughthe tie-point TP1. To control the power delivered or received, theoperator merely adjusts the manual control knob 29 which moves thepointer of the power indicator 3) to the desired power position. The tapof the potentiometer PT aise moves to a new position on thepotentiometer PT since the parts are mechanically connected together bythe mechanical link 31. The voltage supplied by the tap of thepotentiometer PT is then applied to the current generator GT introducinga current at point 32 in the transmission system resistor network.

When this procedtue has been followed in each of the stations and thetie-point TP1, it must be repeated until all three nulls are zerosimultaneously, then it is merely necessary to read the value of thepower indicated by the power indicators S, 17 and 21, in order to inturn adjust each of the stations l, 2, and 3 in the actual power systemto correspond with power settings indicated by this computer.

In order to provide automatic operation of the economic dispatchcomputer in FIGURE l, it is merely necessary to provide several motors33, 34 and 3S on the shafts 7, 15 and 19, respectively. The motors 33,34 and 3S are provided with control ampliiers 36, 37 and 38,respectively, capable of receiving an output from across each of thenull meters N1, N2 and N3, C2 and C3 respectively, in order to drive themotors 33, 34 and 3S, respectively in response to the positive ornegative difference voltage indicated by each null meter. Any unbalancein the amplitier inputs indicating the difference voltages inthe nullmeters will thus cause the motors to drive their associated stationshafts in a direction and to a position of zero diterence voltagepresenting a null indication in the null indicators N1, N2 and N3.

The circuit of FIGURE 2 also provides an automatic means for determiningthe incremental worth setting of CT for the system. This function isdetermined by the comparison of the total power desired for the systemagainst the summation of the powers supplied by each of stations and thetie-point TP1. In order to accomplish this, the shaft 2 of theincremental worth potentiometer CT is provided with the motor drive 43controlled by a motor control summing ampliiier 44. The motor controlsumming amplifier is provided with an input to the ampliiier from apotentiometer 45 driven by a mechanical link 46 having a manual controlknob 47 and a total power indicator 48. The potentiometer 45 is placedacross a source of power 49 for developing a voltage across thepotentiometer representative of the total power needed for the system.The operator knowing the total power or knowing the interchange ofpower, plus or minus between his system and other systems, indicatingthe needed power system adjustment, adjusts the manual control knob 47positioning the pointer of the indicator 48 and the variable tap of thepotentiometer 45 to the known total power or zero interchange powerlevel. The potentiometer 45 then supplies a control voltage over theconductor 50 to the summing control amplifier 44.

The summing ampliiier 44 -is also provided with an input from each ofthe power potentiometers P1 through P3 of each of the stations l through3 and a tie-point TPI. For example, the voltage ,from the variable tapof potentiometer P1 and supplied through the conductor 51 to the summingampliiier 44, similarly the conductors 52 and 53 supply the voltagereferences from the potentiometers P2 and P3 respectively, of stations 2and 3 of the summing amplifier 44. In addition, the conductor 54provides Yan input voltage to the summing ampli'lier V44 from thetie-point potentiometer PT which is also used to indicate the totalpower supplied or received from the tie-point TPl. The voltages from theconductors 56 through 54 are then algebraically combined in the summingamplilier 44 and used to readjust the control motor 43 for the incrementpotentiometer CT. Any readjustment of the potentiometer Cr providescontrol signals to the amplifiers 36, V317 and 38 for controlling themotors 33, 34 and 35 to readjust the power settings of each of thestations in the system. This, in turn dictates a readjustment of theincremental cost potentiomeer CT through the `motor 43, since the totalvalue o power delivered to each'of the stations is changed which in turneffects the summing amplifier 44 controlling the motor 43. Thisadjustment continues automatically until the total power deilvered bythe stations and ties equals the total power indicated by thepotentiometer 45. The system will then v balance.

If it is desired to determine the worth of incremental delivered powerat any of the station delivering points in the network, such as thepoint A, the point 26, or the point 27,V as desired, the worth ofincremental delivered power meter SS connected between the point S6 ofthe incremental cost potentiometer group and the selected point can beused. This meter will then indicate the Worth of incremental powerdelivered to the particular point being observed.

Although several embodiments of this invention have bten disclosedherein, it will .be appreciated by those skilled in the art, thatvarious modiiications in the details of the computer herein disclosed,together with the organization of the components may be made withoutdeparting from the spirit and scope of the invention.

I claim as my invention:

1. An economic dispatch computer for a power distribution systeminvolving a network connecting a plurality of stations comprising meansfor each station for producing a current proportional to the tot-alpower production of that station, means for each station for producing avoltage propontional to the incremental cost of said total powerproduction of that station, impedance means proportional to the actualnetwork resista-ness interconnecting said stations, said impedance meansconnected to said iirst mentioned means for providing voltage changesbetween stations proportional to the incremental losses in the network.

2. An economic dispatch computer for a power distribution systeminvolving a network connecting a plurality of stations comprising meansfor each station for producing a current proportional to the total powerproduction of that station, means for each station for producing avoltage proportional to the incremental cost of said total powerproduction of that station, impedance means proportional to the actualnetwork resistances interconnecting said stations, said impedance meansconnected to said iirst mentioned means'for providing volta ge changesbetween stations proportional tothe incremental losses in the networkfor allowing all station incremental delivered power costs -to be thesame at a given reference point in said system.

' 3.- AnV economic dispatch computer for a power distribu-tion systeminvolving a network connecting a plurality of stations comprising meansfor each station for producing a current proportional tothe total powerproduction `of Vthat stat-ion, means for each station for producing avoltage proportional to the incremental cost of said total powerproduction of that station, impedance meansY proportional to the actualnetwork resistances interconnecting said stations, said impedance meansconneoted to said drst mentioned means providing voltage changes betweenstations proportional to the incremental losses in the network forallowing all station incremental delivered power costs to be the same ata given reference point in said system,- :totalizing circuit means forconnecting said ii-rstY mentioned means for each station together toprovide total power indication output for the system.

4. An economic dispatch computer for a power distribution systeminvolving a network connecting a plurality of stations comprising meansfor each station for producing a current proportional to the total powerproduction of that station, means for each station for producing avoltage proportional to the incremental cost of said total powerproduction of that station, impedance means proportional to the actualnetwork resistances interconnecting said stations, said impedance meansconnected to said first mentioned means providing voltage changesbetween stations proportional to the incremental losses in the networkfor allowing all station incremental delivered power costs to be thesame at a given reference point in said system, totalizin-g circuitmeans for connecting said rst mentioned means for each station togetherto provide total power indication output for the system, and total powerselecting means for establishing a desired total power output for saidsystem.

5. An economic dispatch computer for a power distri- -butiou systeminvolving a network connecting a plurality of stations comprising meansfor each station for producing a current proportionalV to the totalpower production of that station, means for each station for producing aVoltage proportional to the incremental cost of said total powerproduction of that station, impedance means proportional to the actualnetwork resistances interconnecting said stations, said impedance meansconnected to said rst mentioned means providing voltage changes betweenstations proportional to the incremental losses in the network forallowing all station incremental delivered power costs to he the same ata given reference point in said system, totalizing circuit means forconnecting said first `mentioned means for each station together toprovide total power indication output for the system, total powerselecting Ymeans for establishing a desired total power output-for saidsystem, and control means for comparing said total power selecting meansand said totalizing circuit means, said control means being capable ofcausing each said first mentioned means for each station to readjust toa selected total power selecting means.

References Cited in the le oi this patent UNITED STATES PATENTS2,650,760 Bins sept. t, 1953 2,829,829,V Starr et al Apr. 8, 19582,836,730 Early May 27, s 2,836,731 Miner May 27, 195s 2,962,598 Larewet al Nov. 29, 1960 vOTHER REFERENCES Brownlee:V Coordination ofIncremental Fuel Costs, AIEE Trans., part III, A vol. 73, lune 1954, pp,523-533.

